The relevant part of the quote:
Only once had she put the doctrine of non-interference into practice,
This is an example of "subject-auxiliary inversion", where the auxiliary verb ("had") is moved in front of the subject. The reason for the move is that the introductory phrase "only once" has negative force.
Wikipedia "subject-auxiliary inversion"
Another use of subject–auxiliary inversion is in sentences which begin with certain types of expressions which contain a negation or have negative force. For example,
a. Jessica will say that at no time.
b. At no time will Jessica say that. -Subject-auxiliary inversion with a fronted negative expression.
Linked from that Wikipedia article is this one, expanding on the subject:
Wikipedia "negative inversion"
In linguistics, negative inversion is one of many types of subject–auxiliary inversion in English. A negation (e.g. not, no, never, nothing, etc.) or a word that implies negation (only, hardly, scarcely) or a phrase containing one of these words precedes the finite auxiliary verb necessitating that the subject and finite verb undergo inversion.
So, in your example, you could start with a non-inverted form:
She had put the doctrine of non-interference into practice only once...
and invert it:
Only once had she put the doctrine of non-interference into practice...
In this case, either form is grammatical. It's the negative sense of "only once" that allows the inversion.